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Question

The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire and passing through the centre of mass of the system :

A
Mr2(14π2)
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B
Mr2(1+4π2)
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C
Mr2(1π24)
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D
Mr2(1+π24)
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Solution

The correct option is C Mr2(14π2)
Isemicircle=12Icircle=12Mcircler2=Msemicircler2
But, Isemicircle=Icm+Msemicircle(2rπ)2 where 2rπ is the distance of the com from the centre of the semicircle.

Icm=IsemicircleMsemicircle(2Rπ)2=Msemicircler2Msemicircle(2rπ)2=Msemicircler2(14π2)

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